Relation between output transfer characteristic and step input response

[Michael Robinson]

Consider a current source circuit with an output transfer characteristic
that has a spot where it has an angle or kink, like this (view with
non-proportional font):

______
/
/
/
/

I was looking at a current source circuit with an output curve that looks
just like that.
When you turn it on, in other words when you subject it to a step input, it
rings like mad.
I found a way to modify the circuit so it doesn't have a kink in the
transfer characteristic;
the new circuit's curve looks like a transistor output. The current rise
looks
parabolic and it merges smoothly into the part where it levels off.
I simulated the new circuit; it doesn't ring when subjected to a step input.
I can understand that the circuit with the smooth output characteristic is
more stable,
and the simulation demonstrated that. Now this has got me wondering about
the
mathematical connection between a circuit's output transfer characteristic
and the input step response.
It seems that when the output characteristic isn't smooth (differentiable)
the circuit has a stability problem.
But how to go about justifying it analytically?

 

[Tim Williams]

Look at AC, not DC parameters for clues. The DC transfer function can be
any crazy thing and still oscillate -- or not.

Tim

 

[josephkk]

I have modified the pulse sources in PSpice such that rising and
falling edges are the TANH function, smooth like most real sources.

...Jim Thompson

Personally, i would keep the option for trapezoidal pulse sources as well.

?-)

 

[Tim Williams]

Yep. I've gone a bit "TANH-crazy" with _virtually_all_ of the
behavioral models I've created. Bye, bye convergence problems.

Strange. I've written TANH transfer curves before (basically to simulate
logic elements) and fairly often had them produce bizarre errors, namely,
singular matrix and divide by zero.

Tim